Gauge Theory and Variational Principles

A detailed and self-contained mathematical account of gauge theory, this text is geared toward beginning graduate students and advanced undergraduates. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index. 1981 ed.